Let G be a group acting geometrically on a CAT(O) space X. We show that if c E ax is a cut point, then there is an infinite torsion subgroup of G which fixes c. In particular if G is virtually torsion free, if X is a Euclidean cube complex, or if X is 2-dimensional, then ax has no cut point.We also show that if G is a group acting geometrically on a CAT(O) space X, then G has an element of infinite order.

Abstract. Let G be a one-ended group acting discretely and co-compactly on a CAT(0) space X. We show that ∂X has no cut points and that one can detect splittings of G over two-ended groups and recover its JSJ decomposition from ∂X.We show that any discrete action of a group G on a CAT(0) space X satisfies a convergence type property. This is used in the proof of the results above but it is also of independent interest. In particular, if G acts co-compactly on X, then one obtains as a Corollary that if the Tits diameter of ∂X is bigger than 3π 2 then it is infinite and G contains a free subgroup of rank 2.

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We present results from a study of genetic variation in Utah's cougar population. Estimates were based on data for 50 animals at nine microsatellite loci with five individuals sampled for each of ten management units throughout Utah. Levels of variation were moderate (average genetic diversity across populations was estimated to be 0.4687 for all 50 individuals), and comparable with other large mammals. But this level of variation for the microsatellite loci translated into an inbreeding effective population size of only 571 animals, much lower than the current estimates of census sizes of around 2000-3000. A lack of differentiation among the sampled populations across Utah (average N e m = 6.2) indicates that gene flow occurs over a large area. Since cougars are capable of movement beyond the Utah state borders (and certainly across management units), a better understanding of migration rates and patterns of dispersal will be achieved by sampling a much larger geographic region incorporating much of the western USA. Successful management and conservation of this species will then require a far more integrated approach, involving agencies across a number of states, as opposed to current management practices involving individual units within states.

We show how to associate an ‫-ޒ‬tree to the set of cut points of a continuum. If X is a continuum without cut points we show how to associate an ‫-ޒ‬tree to the set of cut pairs of X . 54F15, 20E08; 54F05, 20F65